Twistor transform of all tree amplitudes in N=4 SYM theory

Abstract

We perform the twistor (half-Fourier) transform of all tree n-particle superamplitudes in N=4 SYM and show that it has a transparent geometric interpretation. We find that the N^kMHV amplitude is supported on a set of (2k+1) intersecting lines in twistor space and demonstrate that the corresponding line moduli form a lightlike (2k+1)-gon in moduli space. This polygon is triangulated into two kinds of lightlike triangles lying in different planes. We formulate simple graphical rules for constructing the triangulated polygons, from which the analytic expressions of the N^kMHV amplitudes follow directly, both in twistor and in momentum space. We also discuss the ordinary and dual conformal properties and the cancellation of spurious singularities in twistor space.

46 pages, 17 figures

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• Symmetries and analytic properties of scattering amplitudes in N=4 SYM theory
• Superconformal invariants for scattering amplitudes in N=4 SYM theory
• Twistor-Strings, Grassmannians and Leading Singularities
• On MHV Form Factors in Superspace for $\mathcal{N}=4$ SYM Theory
• Unraveling L_{n,k}: Grassmannian Kinematics
• A First Course on Twistors, Integrability and Gluon Scattering Amplitudes
• Einstein supergravity amplitudes from twistor-string theory
• A Direct Proof of BCFW Recursion for Twistor-Strings
• Inverse Soft Factors and Grassmannian Residues
• Cross-Order Integral Relations from Maximal Cuts
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• On the Classification of Residues of the Grassmannian
• Complete Equivalence Between Gluon Tree Amplitudes in Twistor String Theory and in Gauge Theory
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Yangian Symmetry in N=4 super Yang-Mills
• Obtaining One-loop Gravity Amplitudes Using Spurious Singularities
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• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes
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• A Celestial Description of Planar Super-Yang-Mills Theory
• Delta functions on twistor space and their sign factors
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